4,127 research outputs found
Median problems in networks
The P-median problem is a classical location model “par excellence”. In this paper we, first examine the early origins of the problem, formulated independently by Louis Hakimi and Charles ReVelle, two of the fathers of the burgeoning multidisciplinary field of research known today as Facility Location Theory and Modelling. We then examine some of the traditional heuristic and exact methods developed to solve the problem. In the third section we analyze the impact of the model in the field. We end the paper by proposing new lines of research related to such a classical problem.P-median, location modelling
A Framework for Globally Optimizing Mixed-Integer Signomial Programs
Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York
Linear/Quadratic Programming-Based Optimal Power Flow using Linear Power Flow and Absolute Loss Approximations
This paper presents novel methods to approximate the nonlinear AC optimal
power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF
problems that can be used for power system planning and operation. We derive a
linear power flow approximation and consider a convex reformulation of the
power losses in the form of absolute value functions. We show four ways how to
incorporate this approximation into LP/QP based OPF problems. In a
comprehensive case study the usefulness of our OPF methods is analyzed and
compared with an existing OPF relaxation and approximation method. As a result,
the errors on voltage magnitudes and angles are reasonable, while obtaining
near-optimal results for typical scenarios. We find that our methods reduce
significantly the computational complexity compared to the nonlinear AC-OPF
making them a good choice for planning purposes
A NOTE ON FIXING MISBEHAVING MATHEMATICAL PROGRAMS: POST-OPTIMALITY PROCEDURES AND GAMS-RELATED SOFTWARE
Mathematical programming formulations can yield faulty answers. Models can be unbounded, infeasible, or optimal with unrealistic answers. This article presents techniques for theory-based discovery of the cause of faulty models. The approaches are demonstrated in the context of linear programming. They have been computerized and interfaced using the General Algebraic Modeling System (GAMS), and are distributed free of charge through new GAMS versions and an outline web page.Debugging, GAMS software, Mathematical programming, Research Methods/ Statistical Methods,
Randomized Low-Memory Singular Value Projection
Affine rank minimization algorithms typically rely on calculating the
gradient of a data error followed by a singular value decomposition at every
iteration. Because these two steps are expensive, heuristic approximations are
often used to reduce computational burden. To this end, we propose a recovery
scheme that merges the two steps with randomized approximations, and as a
result, operates on space proportional to the degrees of freedom in the
problem. We theoretically establish the estimation guarantees of the algorithm
as a function of approximation tolerance. While the theoretical approximation
requirements are overly pessimistic, we demonstrate that in practice the
algorithm performs well on the quantum tomography recovery problem.Comment: 13 pages. This version has a revised theorem and new numerical
experiment
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